一种模拟最速下降法的表面网格优化方法  

An Analogue of Steepest Decent Method for Surface Mesh Smoothing

作　　者：高爽[1] 郑耀[1] 

机构地区：[1]浙江大学工程与科学计算研究中心

出　　处：《江南大学学报（自然科学版）》2005年第5期446-450,共5页Joural of Jiangnan University (Natural Science Edition)　

基　　金：国家杰出青年科学基金项目(60225009)资助课题

摘　　要：提出的ADAW方法是一种基于优化原理的网格光滑化方法.它模拟最速下降法的过程,针对局部网格优化这个多目标优化问题,根据最速下降法的两个步骤对目标函数的连续或可导的要求,设计了一对目标函数(可导函数和连续不可导函数),共同作用于网格光滑化过程.可导函数用于计算局部网格单元质量平均值;连续不可导用于计算最差单元质量和质量平均值的差.在寻找最速下降方向时,计算可导目标函数的梯度,得到最值所在方向;在线性搜索过程中,同时使用两种目标函数确定步长.给出了用于结合ADAW方法和Laplacian方法的完整算法,用于提高光滑化效率.实验结果证明,该方法在提高局部网格平均质量的同时,也改善了最差单元的质量,整体处理效果优于传统方法.ADAW, a new optimization-based smoothing method proposed in this paper, is an analogue of steepest decent method. Based on requirements of objective functions in the steepest decent method, the new method solves a multiobjective optimization problem of local mesh smoothing by designing a pair of objective functions, and adjusts the locations of vertices by properly combining the optimization of them. The first function calculates the average value of elements quality, and the second one is used to measure the disparity between the worst element ＂s quality and the average value of the local mesh. In the course of the Steepest Decent Method, the former one, which has derivative function, is used to get the directions of the optimal points, and when it comes to computing steps, which only requires the continuity of functions, both functions are used to get the final result. An overall scheme of combining ADAW and Laplacian method is also presented in this paper and is used to get better efficiency. The result of numerical experiments shows that the new method can enhance the quality of local mesh as well as improve the quality of the worst element, and it outperforms the existing methods significantly.

关 键 词：有限元网格 网格光滑化 基于优化原理的网格光滑化 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]